A plane electromagnetic wave varies sinusoidally at 92.2 MHz as it travels throu

Question

A plane electromagnetic wave varies sinusoidally at 92.2 MHz as it travels through vacuum along the positive x direction. The peak value of the electric field is 2.12 mV/m, and it is directed along the positive y direction.

(a) Find the wavelength.
m

(b) Find the period.
ns

(c) Find the maximum value of the magnetic field.
pT

(d) Write expressions in SI units for the space and time variations of the electric field. (x is in meters, and t in seconds.)

Write expressions in SI units for the space and time variations of the magnetic field. (x is in meters, and t in seconds.)

(e) Find the average power per unit area this wave carries through space.
W/m2

(f) Find the average energy density in the radiation.
J/m3

(g) What radiation pressure would this wave exert upon a perfectly reflecting surface at normal incidence?
Pa

Explanation / Answer

frequency f =92.2x10^6 Hz
E0 =2.12 mV/m along y-axis
a)
wavelenght = speed/freq =3x10^8/92.2x10^6 =3.25 m
b)
peroid = 1/f = 1/92.2x10^6 =10.8 ns
c)
B0=E0/c =2.12x10^-3/3x10^8 = 7.06x10^-12 T
d)

so
E =(2.12x10^-3) cos2pi[x/3.25 -92.2x10^6] V/m
along +y-axis
e)
B = (7.06x10^-12 ) cos2pi[x/3.25 -92.2x10^6] T
along +z-axis

e)
the average power =E0*B0/mu_0
P =2.12x10^-3*7.06x10^-12/4pix10^-7 =1.2x10^-8 W/m^2
f)
average energy density =e_0*E^2 =
u =8.845x10^-12x(2.12x10^-3)^2 =3.975x10^-17 J/m^3
g)
radiation pressure = u/2 =1.98x10^-17 Pa

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